A Modified Subgradient Extragradeint Method For Variational Inequality Problems And Fixed Point Problems In Real Banach Spaces

ABSTRACT

Let E be a 2-uniformly convex and uniformly smooth real Banach space with dual space E ∗ . Let A : C → E ∗ be a monotone and Lipschitz continuous mapping and U : C → C be relatively nonexpansive. An algorithm for approximating the common elements of the set of fixed points of a relatively nonexpansive map U and the set of solutions of a variational inequality problem for the monotone and Lipschitz continuous map A in E is constructed and proved to converge strongly.